If you solve the equation first for y and get y = -1 / (6x - x^2) + C, this C value will be different.

Which way is correct or

------------------------------------------------------------------------ !!!! should the C value remain the in the denominator? !!!! ------------------------------------------------------------------------- Yes, the C must remain in the denominator. Your solution is

-1/y = 6x - x^2 + C and when you invert and multiply by

minus one, the whole expression goes to the denominator. The constantremains the same in both cases.

While I don't have the examination, it is clear that the DE involves ay^2 term. Squaring (-1/(6x-x^2)) + C and (-1/(6x-x^2 +C))will give you two entirely different results.

In general, when you obtain a solution that you are not comfortablewith, it is worthwhile to check back and see if it fits the original DE.